Identify the side lengths of the following triangle.

The simplified formula is therefore [tex](p^2 + 31p - 140) / 9p^3 (p - 10)[/tex] as factor the first fraction's numerator and discover a shared denominator.

A fraction is a percentage of an entire amount or a ratio of two numbers. It is a means to express a numeric value that is neither a whole number nor an integer. The number at the top of a fraction is called the numerator, while the number at the bottom is called the denominator. The denominator is the entire amount of elements of the entirety or the ratio's divisor, while the numerator is the portion that makes up the entirety or ratio that is being evaluated.

given

We must factor the first fraction's numerator and discover a shared denominator for the two fractions in order to simplify this expression:

(p² + 17p + 70) / 9p³ + 63p² * 3 / (p + 10)

= (p + 10)(p + 7) / 9p³ + 189p² / (p + 10)

= (p + 10)(p + 7); 9p3 + 189p2; (p - 10)/(p + 10); (p - 10)

= 189p2(p - 10)/9p3(p + 7)/9p3(p + 10) (p - 10)

= [(p + 10)(p + 7) + 21p²(p - 10)] / 9p³(p - 10) (p - 10)

= [(p² + 31p - 140) / 9p³(p - 10)]

The simplified formula is therefore [tex](p^2 + 31p - 140) / 9p^3 (p - 10)[/tex] as factor the first fraction's numerator and discover a shared denominator.

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A) The explicit rule for the value of the collection n years after it was worth $300,000 is  = $300,000 * (1.15)^n

B) Rounded to the nearest dollar, the value of Madame Dumas's art collection 7 years after she started tracking its worth is $698,285.

A) We know that the value of the art collection three years ago is $300,000, and the value of the collection two years ago is $345,000. Using these values, we can find the common ratio (r) of the geometric sequence:

r = (value two years ago) / (value three years ago)

r = 345,000 / 300,000

r = 1.15

Now that we have the common ratio, we can write the explicit rule for the value of the collection n years after it was worth $300,000:

value after n years = $300,000 * (1.15)^n

B) Using the explicit rule we found in part A, we can determine the value of the collection 7 years after it was worth $300,000:

value after 7 years = $300,000 * (1.15)^7

value after 7 years ≈ $698,285

Rounded to the nearest dollar, the value of Madame Dumas's art collection 7 years after she started tracking its worth is $698,285.

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According to the information, to estimate the total cost for a 50-kilometer taxi ride by extending the line to a distance of 50 kilometers and reading off the corresponding y-value, which is approximately $105.00.

Distance (km) Total Cost ($)

0 5.00

1 7.00

2 9.00

3 11.00

4 13.00

5 15.00

b. The graph of the total cost C as a function of the distance d up to 10 kilometers is a linear function with a slope of $2.00/km and a y-intercept of $5.00.

The start value of the total cost is $5.00, which is the initial fee charged by the taxi service. The rate of change is $2.00/km, which is the cost per kilometer travelled.

The equation that models the total cost C of using the taxi service for a distance of d kilometers is:

Using the equation from part d, we can calculate the total cost of a 50-kilometer taxi ride:

Alternatively, we could use the graph to estimate the total cost for a 50-kilometer taxi ride by extending the line to a distance of 50 kilometers and reading off the corresponding y-value, which is approximately $105.00.

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A shop is open 9 am - 7 pm. the function r(t), graphed above, gives the rate at which customers arrive (in people/hour) at time t, the line will vanish at 9 am + 2.5 hours = 11:30 am.

Since the salespeople can serve customers at a rate of 75 people per hour, the net rate at which customers are added to the line is given by:

Net rate = R(t) - 75

where R(t) is the rate at which customers arrive.

The line will vanish when the net rate becomes zero, which means that the rate at which customers are added to the line is equal to the rate at which they are served. Thus, we have:

R(t) - 75 = 0

Solving for t, we get:

R(t) = 75

Looking at the graph, we can see that R(t) is equal to 75 at approximately 2.5 hours after 9 am. Therefore, the line will vanish at 9 am + 2.5 hours = 11:30 am.

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We have to make a suspicion based on the given data. The standard deviations of the three bunches are not given within the address, so we cannot straightforwardly decide whether the condition of equal standard deviations is met. Be that as it may, ready to make a few taught surmises based on what we know almost each gather.

The primary gather, which did not think about, is likely to have a bigger change in scores than the other two bunches since understudies with shifting levels of arrangement and capacity took the test. Subsequently, we might anticipate the standard deviation of this group to be bigger than that of the other two bunches.

It is conceivable that the condition of rise to standard deviations isn't met. In case the condition of equal standard deviations isn't met, we may require to utilize an altered adaptation of ANOVA, such as Welch's ANOVA, which does not expect a rise in changes. 

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The sets of transformations that result in the same image when performed in any order are:

Translation, dilation with center (0,0)

Two translations

In mathematics, a transformation refers to a process that changes the size, shape, position, or orientation of a geometric figure or an object in a coordinate plane or space. There are several types of transformations, such as translation, rotation, reflection, and dilation, which are used to alter the original figure to create a new one that is similar or congruent to the original. Transformations are used in geometry, algebra, and other branches of mathematics to study and understand various properties of geometric shapes and objects.

Here,

For the first set, if we perform a translation followed by a dilation with center (0,0), the result will be the same as if we perform the dilation first followed by the translation. This is because the dilation does not change the direction of the translation, and the center of dilation is at the origin, so the translation is unaffected.

For the second set, any two translations can be combined to form a single translation, so the order in which they are performed does not matter.

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For a survey to put an estimate the proportion of voters who support gun control, the minimum sample size is 752 that is minimum 752 people need to be included in the sample.

We have a survey which is planned to estimate the proportion of voters who support gun control. Margin of error, MOE = 3% = 0.03

Confidence level = 90% = 0.90

No information about the proportion of the voters that is p,so let's assume, p= 0.5

Level of significance, α = 1 - CI

= 1 - 0.90 = 0.10

We have to determine the sample size of people. Using the following formula for computes minimum sample size required to estimate population proportion within the required margin of error, [tex]n ≥ p( 1-p) (\frac{z_c}{MOE})²[/tex]

where, n --> sample size

[tex]z_c[/tex]--> critical value of z

using the Z-distribution table, the value of z for 90% confidence interval is 1.64.

Substitute all known values in above formula, [tex]n ≥ 0.5( 1- 0.5) (\frac{1.64}{0.03})²[/tex]

= 751.54 ~ 752( people must be a integer no.)

Hence, required minimum sample size is 752.

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Sample a is more surprising because there is more variability in smaller samples, making it less likely to obtain a sample mean that is as extreme as $2750.

Sample A is more surprising because there is more variability in smaller samples. The variability of sample means decreases as the sample size increases due to the central limit theorem.

The central limit theorem states that as the sample size increases, the distribution of sample means becomes more normal, with a mean equal to the population mean and a standard deviation equal to the population standard deviation divided by the square root of the sample size.

Therefore, sample A, which has a smaller sample size of 9, has a larger standard deviation and more variability in the mean award amount compared to sample B, which has a sample size of 36. It is less likely to obtain a sample mean of $2750 from a smaller sample with more variability than from a larger sample with less variability. Thus, sample A is more surprising than sample B.

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Answer:

$14.73

Step-by-step explanation:

To find out how much you made per hour, you need to divide your total earnings by the total number of hours worked. 15 weeks at 25 hours per week is a total of 375 hours. Dividing $5,525 by 375 gives you $14.73 per hour. Therefore, you made approximately $14.73 per hour. Remember to round your answer to the nearest cent, so the final answer will be $14.73.

Answer:

$5,525/(15 hrs/wk × 25 wks)

= $5,525/375 hrs = $14.73/hr

In computer programming, variables are used to store and manipulate data. In this case, an int variable named strawsoncamel has been declared and assigned a value.

To increase the value of strawsoncamel by 1, you can use the increment operator (++). This operator adds 1 to the current value of the variable and assigns the result back to the variable.

For example, if strawsoncamel has a value of 5, the statement strawsoncamel++; would increase its value to 6. This can be useful in many scenarios, such as counting or iterating through a loop. It's important to note that the increment operator can also be used in other ways, such as ++strawsoncamel, which increments the value of the variable before it is used in an expression.

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To increase the value of the variable strawsoncamel by 1, you can use the increment operator "++". So the statement would be:
strawsoncamel++;

This will increment the value of strawsoncamel by 1. The increment operator is an example of an operator in programming, which performs a specific operation on a variable. In this case, it increases the value of the variable by 1, which is also known as an increment.
To increase the value of the integer variable `strawsoncamel` by 1 using the increment operator, follow this step:
Write the statement: `strawsoncamel++;`
This line of code will use the increment operator (`++`) to increase the value of the variable `strawsoncamel` by 1.

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The quadrilateral ABCD has been reflected across the line x=2 to form its image, as can be seen in the provided figure.

A quadrilateral is a closed object with four successive sides that is referred to as a four-sided polygon in geometry. A quadrilateral's internal angles are always added up to 360 degrees. There are numerous varieties of quadrilaterals, such as: A hexagon with two sets of parallel sides is called a parallelogram. A trapezoid with four sharp angles is a rectangle. a rectangles with four equal sides is referred to as square. A parallelogram with one of the parallel sides is called a trapezium (or a trapezoid in American English). A trapezoid with two adjacent sets of equal-length sides is referred to as a kite.

given

The quadrilateral ABCD has been reflected across the line x=2 to form its image, as can be seen in the provided figure.

Thus, the appropriate answer is: Refraction along the line x=2

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The constant function and quadratic function intersect at one point in the nonlinear system.

In a nonlinear system with a constant function and a quadratic function, the two graphs intersect at one point, indicating the solution to the system. The constant function represents a horizontal line, while the quadratic function represents a parabola.

The point of intersection represents the solution where the value of the constant function equals the value of the quadratic function. The relationship between the two graphs is that they intersect at this one point, which is the unique solution to the system

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The only prism with a volume between 10 and 20 cubic inches is Prism C, which has a volume of 16 cubic inches.

To find the volume of each prism, we need to use the formula of volyume for prisms which is: Volume = Base Area x Height. Now we will go ahead to find the volumes for all the prisms as follows:

Prism A:

Base Area = 4 x 5 = 20

Height = 2

Volume = 20 x 2 = 40 cubic inches

Prism B:

Base Area = 3 x 4 = 12

Height = 3

Volume = 12 x 3 = 36 cubic inches

Prism C:

Base Area = 4 x 4 = 16

Height = 1

Volume = 16 x 1 = 16 cubic inches

Prism D:

Base Area = 4 x 4 = 16

Height = 6

Volume = 16 x 6 = 96 cubic inches

So, the prism whose volume falls between 10 to 20 is the third prism.

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The value of x in the triangle is 8.8493 units.

Trigonometry deals with the relationships between the sides and angles of triangles.

The three primary trigonometric functions are sine, cosine, and tangent, which are ratios of the sides of a right triangle. These functions are often abbreviated as sin, cos, and tan.

Using the given triangle:

11.6² =  x² + 7.5²    (Pythagoras theorem)

x² = 11.6² - 7.5²

x² = 78.31

x = √78.31

x = 8.8493 units

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The midpoint between [tex]-3,5 and 1,6 is (-1,5.5)[/tex]

The midpoint between two points can be found by averaging the coordinates of the points separately for each dimension (x-axis and y-axis). Let's calculate the midpoint between [tex]-3,5 and 1,6[/tex].

The coordinates of the two points are:

Point 1: ([tex]-3,5[/tex])

Point 2: ([tex]1,6[/tex])

To find the midpoint, we can average the x-coordinates and y-coordinates separately.

Midpoint's x-coordinate = (x-coordinate of Point [tex]1[/tex] + x-coordinate of Point [tex]2[/tex]) / [tex]2[/tex]

Midpoint's y-coordinate = (y-coordinate of Point [tex]1[/tex] + y-coordinate of Point [tex]2[/tex]) / [tex]2[/tex]

According to the problem

Midpoint's x-coordinate = [tex](-3+1)/2= -2/2= -1[/tex]

Midpoint's y-coordinate = [tex](5+6)/2= 11/2 = 5.5[/tex]

So, the midpoint between [tex]-3,5[/tex] and [tex]1,6[/tex] is [tex](-1,5.5)[/tex].

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The emission of CO₂ after 14 years will be 52755 KT.

Given that, the emissions of CO₂ is 70,000 KL, will decrease at the rate of 2% per year for 14 years,

So,

Emission (E₀) for 14t year = 70,000 × (1-0.02)¹⁴

= 70000 × 0.75
= 52755

Hence, the emission of CO₂ after 14 years will be 52755 KT.

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The bacterial count after 48 hours decreases. A correlation coefficient of 0 would indicate no relationship between the two variables.

To find the correlation between the bacterial count after 24 hours and 48 hours, we would need the actual numerical values of the bacterial counts for each strain. Without that information, we cannot calculate the correlation coefficient. However, it is important to note that a positive correlation would indicate that as the bacterial count after 24 hours increases, the bacterial count after 48 hours also increases. A negative correlation would indicate that as the bacterial count after 24 hours increases, the bacterial count after 48 hours decreases. A correlation coefficient of 0 would indicate no relationship between the two variables.

The complete question is-

Five strains of the Staphylococcus aureus bacteria were grown for 24 hours either at 35 degrees Celsius or at 43 degrees Celsius. Here are the resulting bacterial counts for each condition:

24 hr: 66, 71, 93, 102, 62

48hr: 110,123,146,136,113

If we had plotted bacterial count at 35 degrees Celsius on the y-axis instead of the x-axis, the value of the correlation coefficient would be

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The interpretation of the slope is On average, for every additional year of age, bone density loss increases by approximately 0.41. (option a)

To calculate the least squares regression line, the data points are first plotted on a scatter plot. The line of best fit is then drawn through the data points such that the sum of the squared distances between the line and the data points is minimized. The slope of this line can be calculated using the following formula:

slope = (nΣ(xy) - ΣxΣy) / (nΣ(x²) - (Σx)²)

where n is the number of data points, Σ represents the sum of the values, x represents age, y represents bone density loss, and xy represents the product of x and y.

Using this formula, the slope for this data set can be calculated to be approximately 0.41. This means that, on average, for every additional year of age, bone density loss increases by approximately 0.41. In other words, the slope indicates a positive relationship between age and bone density loss, with bone density loss increasing as age increases.

Therefore, the correct answer is (a) On average, for every additional year of age, bone density loss increases by approximately 0.41.

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Complete Question:

Osteoporosis is a condition in which bone density decreases, often resulting in broken bones. Bone density usually peaks at age 30 and decreases thereafter. To understand more about the condition, a random sample of women aged 50 and over were recruited. Each woman's bone loss was recorded and the date is shown in this file. Create a scatter plot of these two variables, with age as the x variable and bone density loss as the y variable. Calculate the least squares regression line. What is your interpretation of the slope?

a. On average, for every additional year of age, bone density loss increases by approx 0.41.

b. On average, for every additional one point of bone density loss, age increases by approx 0.41.

c. On average, for every additional year of age, bone density loss increases by approx 6.9.

d. none of the above

The correct statement is:

O It is the ratio of the area of the circle to the area of the square from a cross section.

In the deriving of formula for volume of a cone, it is determined that the volume of the cone equates to one third the volume of the cylinder in which it fits within.

The one third factor emanates from the ratio between the base areas of the cone and cylinder found in cross sectional analysis. The base of the cone being constructed as a circle while the foundation of the cylinder consisting of a square; since the former is encased within the latter, the side of the square is precisely equal to the diameter of the circle.

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Answer:

9.3 ft

Step-by-step explanation:

Answer:

0.06

6/100

Step-by-step explanation:

6% is equivalent to the decimal number 0.06 or the fraction 6/100.

Answer:

6/100 or 0.06

Step-by-step explanation:

hope this helps!

Answer:

Step-by-step explanation:

1) Pythagorean Theorem: a² + b² = c²

4²+b²=5²

b²=5²-4²

b²=25-16

b=√9

b = 3

2) Good Job! Second Question is correct with accurate work shown.

Answer:

Plot (-3, -6). From this point, go up 4 units, then right 5 units, to (2, -2). Plot (2, -2), and then draw a line that goes through these two points.

The columns of A are linearly independent if and only if A has n pivot columns.

Fill in the blank:

If A is an m x n matrix, then the columns of A are linearly independent if and only if A has n pivot columns.

Explanation:

A pivot column of a matrix A is a column that contains a pivot element in the row echelon form of A.

In other words, a pivot column is a column that has a leading non-zero entry in the row echelon form of A.

Suppose A is an m x n matrix with columns. [tex]a1, a2, ..., an[/tex].

If the columns of A are linearly independent, then there is no non-trivial solution to the equation. [tex]c1a1 + c2a2 + ... + cnan[/tex] [tex]= 0[/tex], where [tex]c1, c2, ..., cn[/tex]are not all zero.

This implies that the coefficient matrix.[tex][a1, a2, ..., an][/tex]has full rank n, and so the row echelon form of A has n pivot columns.

Tthe row echelon form of A has n pivot columns, then the coefficient matrix [a1, a2, ..., an] has full rank n.

This implies that the columns of A are linearly independent, because if there were a non-trivial linear combination of the columns of A that gave the zero vector, then the coefficient matrix would not have full rank n.

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Answer:

x = 52.5

Step-by-step explanation:

The sum of the angles of a quadrilateral is 360.

2x+100 +95+60 = 360

Combine like terms.

2x+255=360

Subtract 255 from each side

2x+255-255= 360-255

2x = 105

Divide each side by 2

2x/2 = 105/2

x = 52.5

Answer:

x = 52.5

Step-by-step explanation:

The sum of the interior angles of a quadrilateral is 360°.

Accordingly, let us find the value of x.

2x + 100 + 95 + 60 = 360

2x + 255 = 360

Subtract 255 from both sides.

2x = 360 - 255

2x = 105

Divide both sides by 2.

x = 52.5

A) represents a dilation by a scale factor of 5 with respect to the origin.
B) represents a dilation by a scale factor of 1/5 with respect to the origin.
C) represents a translation 5 units to the right and 5 units up.
D) represents a translation 5 units to the left and 5 units down.

A transformation is a process of changing the position, size, or shape of a geometric object or set of points in the coordinate plane.

The given expressions represent different types of transformations in the coordinate plane:

A) (x, y) → (5x, 5y) represents a dilation, where the image is five times larger than the original point with respect to the origin.

B) (x, y) → (1/5x, 1/5y) represents a dilation, where the image is one-fifth the size of the original point with respect to the origin.

C) (x, y) → (x+5, y+5) represents a translation, where the image is shifted 5 units to the right and 5 units up from the original point.

D) (x, y) → (x-5, y-5) represents a translation, where the image is shifted 5 units to the left and 5 units down from the original point.

In summary:

A) represents a dilation by a scale factor of 5 with respect to the origin.
B) represents a dilation by a scale factor of 1/5 with respect to the origin.
C) represents a translation 5 units to the right and 5 units up.
D) represents a translation 5 units to the left and 5 units down.

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The areas and the surface areas of the figures are calculated below

The area of a figure is the amount of space it occupies in a plane, measured in square units.

So, we have

Figure 1

For the first figure, we have

Area = (2a)² - 1/2 * b² * sin(B)

Evaluate

Area = 4a² - b²sin(B)/2

For the second figure, we have

Area = 18 * 10 + 1/2 * 10 * √(4 * 15² + 18²) + 1/2 * 18 * √(4 * 15² + 10²)

Evaluate

Area = 639.53 square units

Figure 2

Here, we have

Area = 2 * 2 * 2.5 + 2 * 1/2 * 3 * √(3² - 2.5²) + 3 * 2

Evaluate

Area = 20.97

Figure 3 (Stairs)

Here, we have

Area = 8 * 4 + 8 * 8 + 8 * 4 + 8 * 8 + 2 * 16 * 4 + 2 * 8 * 4

Evaluate

Area = 384

Figure 3 (Semi-circular)

Here, we have

Area = 4 * 4 * 6 + 6 * 6 + 2 * 1/2 * (22/7 * (6/2)²) + 1/2 * 2 * 22/7 * (6/2) × 6

Evaluate

Area = 216.86

Figure 3 (Cylinder-Hemisphere-Cone)

Here, we have

Area = 2 * 22/7 * (10/2) * 12 + 22/7 * (10/2) * √(8² - 5²) + 2 * 22/7 * (10/2)²

Evaluate

Area = 632.42

Figure 3 (Cylinder-Cylinder)

Here, we have

Area = 2 * 22/7 * 8 * (8 + 3) + 2 * 22/7 * 2 * (2 + 7) - 22/7 * 2²

Evaluate

Area = 653.71

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Answer: Hi! Read the explanation below:

Brainliest?

Step-by-step explanation:

Let's use the variables x and y to represent the number of bags of soil and plants, respectively, that Katte will buy.

The cost of x bags of soil is $4x, and the cost of y plants is $10y. Therefore, the total cost of Katte's purchases is:

$4x + $10y

We want to make sure that she doesn't spend more than $100, so we can write:

$4x + $10y ≤ $100

We also want to make sure that she buys at least 5 plants, so we can write:

y ≥ 5

Finally, we want to make sure that both x and y are non-negative, since you can't buy negative bags of soil or plants. Therefore, we can write:

x ≥ 0

y ≥ 0

Putting it all together, the system of linear inequalities is:

4x + 10y ≤ 100

y ≥ 5

x ≥ 0

y ≥ 0

To graph this system, we can start by graphing the boundary lines for each inequality. The boundary for 4x + 10y ≤ 100 is the line 4x + 10y = 100, which we can graph by finding two points on the line:

When x = 0, we have 10y = 100, so y = 10. Therefore, one point on the line is (0, 10).

When y = 0, we have 4x = 100, so x = 25. Therefore, another point on the line is (25, 0).

Plotting these two points and connecting them with a line gives us the boundary for 4x + 10y ≤ 100:

       |

   11  |      o

       |

   10  |           o

       |

    9  |              o

       |

    8  |                 o

       |

    7  |                    o

       |

    6  |                       o

       |

    5  |                          o

       |

--------|-----------------------------    

       0    25

The boundary for y ≥ 5 is the horizontal line y = 5. We can graph this line by plotting two points on the line:

When x = 0, we have y = 5, so one point on the line is (0, 5).

When x = 100/4 = 25, we still have y = 5, so another point on the line is (25, 5).

Plotting these two points and connecting them with a line gives us the boundary for y ≥ 5:

lua

       |

       |    

       |

       |    

       |

       |    

    5  |-----------------------

       |

       |

       |

       |

       |

--------|-----------------------------    

       0    25

Finally, the boundaries x ≥ 0 and y ≥ 0 are simply the x and y axes, respectively. We can graph them as:

diff

       |

       |    

       |

       |    

       |

       |    

       |

       |

       |

--------|-----------------------------    

       0    25

Putting it all together, the graph of the system of linear inequalities looks like:

       |

   11  |      o

       |

   10  |           o

       |

    9  |              o

       |

    8  |                 o

       |

    7  |                    o

       |

    6  |                       o

       |

    5  | o----------------------

       |

       |    

       |